Package com.irurueta.numerical.optimization

Class BrentSingleOptimizer

java.lang.Object

com.irurueta.numerical.optimization.Optimizer

com.irurueta.numerical.optimization.SingleOptimizer

com.irurueta.numerical.optimization.BracketedSingleOptimizer

com.irurueta.numerical.optimization.BrentSingleOptimizer

public class BrentSingleOptimizer
extends BracketedSingleOptimizer

This class uses Brent algorithm to determine a local function minimum for single dimension functions. Brent's algorithm will search for a local minimum inside the provided or computed bracket of values. Brent's algorithm is not the fastest among all optimization algorithms, but it is usually one that provides good convergence for most continuous functions. It 's recommended to always set or compute a bracket of values, as the search range is reduced and results usually become more accurate. The implementation of this class is based on Numerical Recipes 3rd ed. Section 10.3. Page 496.

Field Summary

Fields

Modifier and Type	Field	Description
static final double	CGOLD	Is the golden ratio.
static final double	DEFAULT_TOLERANCE	Constant defining the default accuracy of the estimated minimum.
static final int	ITMAX	Is the maximum allowed number of iterations.
static final double	MIN_TOLERANCE	Minimum allowed tolerance.
private double	tolerance	Tolerance value.
static final double	ZEPS	Small number that protects against trying to achieve fractional accuracy for a minimum that happens to be exactly zero.

Fields inherited from class com.irurueta.numerical.optimization.BracketedSingleOptimizer

ax, bx, cx, DEFAULT_MAX_EVAL_POINT, DEFAULT_MIDDLE_EVAL_POINT, DEFAULT_MIN_EVAL_POINT, GLIMIT, GOLD, TINY

Fields inherited from class com.irurueta.numerical.optimization.SingleOptimizer

fmin, listener, resultAvailable, xmin

Fields inherited from class com.irurueta.numerical.optimization.Optimizer

iterationCompletedListener, locked

Constructor Summary

Constructors

Constructor	Description
BrentSingleOptimizer()	Empty constructor.
BrentSingleOptimizer(double minEvalPoint, double middleEvalPoint, double maxEvalPoint, double tolerance)	Constructor.
BrentSingleOptimizer(SingleDimensionFunctionEvaluatorListener listener, double minEvalPoint, double middleEvalPoint, double maxEvalPoint, double tolerance)	Constructor.

Method Summary

Modifier and Type	Method	Description
double	getTolerance()	Returns tolerance value, which is the accuracy to be obtained when a minimum is estimated.
private void	internalSetTolerance(double tolerance)	Internal method to set algorithm tolerance.
boolean	isReady()	Returns boolean indicating whether this instance is ready to start the estimation of a minimum or not.
void	minimize()	This function estimates a function minimum within provided or computed bracket of values.
void	setTolerance(double tolerance)	Sets algorithm's tolerance.

Methods inherited from class com.irurueta.numerical.optimization.BracketedSingleOptimizer

areBracketEvaluationsAvailable, computeBracket, computeBracket, computeBracket, evaluateBracket, getEvaluationAtMax, getEvaluationAtMiddle, getEvaluationAtMin, getMaxEvaluationPoint, getMiddleEvaluationPoint, getMinEvaluationPoint, isBracketAvailable, mov3, setBracket, shift2, shift3, sign

Methods inherited from class com.irurueta.numerical.optimization.SingleOptimizer

getEvaluationAtResult, getListener, getResult, isListenerAvailable, isResultAvailable, setListener

Methods inherited from class com.irurueta.numerical.optimization.Optimizer

getOnIterationCompletedListener, isLocked, setOnIterationCompletedListener

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Details

ITMAX

public static final int ITMAX

Is the maximum allowed number of iterations.

See Also:

• Constant Field Values

CGOLD

public static final double CGOLD

Is the golden ratio.

See Also:

• Constant Field Values

ZEPS

public static final double ZEPS

Small number that protects against trying to achieve fractional accuracy for a minimum that happens to be exactly zero.

See Also:

• Constant Field Values

DEFAULT_TOLERANCE

public static final double DEFAULT_TOLERANCE

Constant defining the default accuracy of the estimated minimum.

See Also:

• Constant Field Values

MIN_TOLERANCE

public static final double MIN_TOLERANCE

Minimum allowed tolerance.

See Also:

• Constant Field Values

tolerance

private double tolerance

Tolerance value. The algorithm will iterate until the result converges below this value of accuracy or until the maximum number of iterations is achieved (and in such case, convergence will be assumed to have failed).

Constructor Details

BrentSingleOptimizer

public BrentSingleOptimizer()

Empty constructor.

BrentSingleOptimizer

public BrentSingleOptimizer(double minEvalPoint,
 double middleEvalPoint,
 double maxEvalPoint,
 double tolerance)
                     throws InvalidBracketRangeException

Constructor. Creates an instance with provided bracket of values.

Parameters:

minEvalPoint - Minimum bracket evaluation point.

middleEvalPoint - Middle bracket evaluation point.

maxEvalPoint - Maximum bracket evaluation point.

tolerance - Tolerance or accuracy to be obtained in estimated minimum.

Throws:

InvalidBracketRangeException - Raised if the following condition is not met: minEvalPoint <= middleEvalPoint <= maxEvalPoint.

IllegalArgumentException - Raised if tolerance is negative.

BrentSingleOptimizer

public BrentSingleOptimizer(SingleDimensionFunctionEvaluatorListener listener,
 double minEvalPoint,
 double middleEvalPoint,
 double maxEvalPoint,
 double tolerance)
                     throws InvalidBracketRangeException

Constructor. Creates an instance with provided bracket of values and a listener to get single dimension function evaluations.

Parameters:

listener - Listener to evaluate a function.

minEvalPoint - Minimum bracket evaluation point.

middleEvalPoint - Middle bracket evaluation point.

maxEvalPoint - Maximum bracket evaluation point.

tolerance - Tolerance or accuracy to be obtained in estimated minimum.

Throws:

InvalidBracketRangeException - Raised if the following condition is not met: minEvalPoint <= middleEvalPoint <= maxEvalPoint.

IllegalArgumentException - Raised if tolerance is negative.

Method Details

getTolerance

public double getTolerance()

Returns tolerance value, which is the accuracy to be obtained when a minimum is estimated. The algorithm will iterate until the result converges below this value of accuracy or until the maximum number of iterations is achieved (and in such case, convergence will be assumed to have failed).

Returns:

Tolerance value.

setTolerance

public void setTolerance(double tolerance)
                  throws LockedException

Sets algorithm's tolerance. The algorithm will iterate until the result converges below this value of accuracy or until the maximum number of iterations is achieved (an in such case, convergence will be assumed to have failed).

Parameters:

tolerance - Tolerance or accuracy to be obtained in estimated minimum.

Throws:

LockedException - Raised if this instance is locked. This instance will be locked while doing some operations. Attempting to change any parameter while being locked will raise this exception.

IllegalArgumentException - Raised if tolerance is negative.

minimize

public void minimize()
              throws LockedException,
NotReadyException,
OptimizationException

This function estimates a function minimum within provided or computed bracket of values. Given a function f, and given a bracketing triplet of abscissas "ax", "bx", "cx" (such that bx is between ax and cx, and f(bx) is less than both f(ax) and f(cx), this routine isolates the minimum to a fractional prevision of about tolerance using Brent's method. The abscissa of the minimum is returned as "xmin", and the function value of the minimum is returned as "fmin", the returned function value.

Overrides:

minimize in class Optimizer

Throws:

LockedException - Raised if this instance is locked, because estimation is being computed.

NotReadyException - Raised if this instance is not ready because either a listener or a bracket has not yet been provided or computed.

OptimizationException - Raised if the algorithm failed because of lack of convergence or because function couldn't be evaluated.

isReady

public boolean isReady()

Returns boolean indicating whether this instance is ready to start the estimation of a minimum or not. The instance is ready when both the listener and the bracket are available.

Overrides:

isReady in class SingleOptimizer

Returns:

True if this instance is ready, false otherwise.

internalSetTolerance

private void internalSetTolerance(double tolerance)

Internal method to set algorithm tolerance. This method does not check whether this instance is locked or not. The algorithm will iterate until the result converges below this value of accuracy or until the maximum number of iterations is achieved (and in such case, convergence will be assumed to have failed).

Parameters:

tolerance - Tolerance or accuracy to be obtained in estimated minimum.

Throws:

IllegalArgumentException - Raised if tolerance is negative.